Optical inspection of liquid crystal variable retarder inhomogeneities

Optimizing near-infrared polariscopic imaging for the living human eye

Hardware architectures and image interpretation can be simplified by partial polarimetry. Mueller matrix (MM) polarimetry allows the investigation of partial polarimeter designs for a given scientific task. In this work, we use MM measurements to solve for a fixed polarization illumination and analyzer state that maximize polariscopic image contrast of the human eye. The eye MM image acquisition takes place over 15 seconds which motivates the development of a partial polarimeter that has snapshot operation. Within the eye, the birefringent cornea produces spatially-varying patterns of retardance exceeding half of a wave with a fast-axis varying from linear, to circular, and elliptical states in between. Our closed-form polariscopic pairs are a general solution that maximizes contrast between two non-depolarizing pure retarder MMs. For these MMs, there is a family of polariscopic pairs that maximize contrast. This range of solutions creates an opportunity to use the distance from optimal as a criteria to adjust polarimetric hardware architecture. We demonstrate our optimization approach by performing both Mueller and polariscopic imaging of an in vivo human eye at 947 nm using a dual-rotating-retarder polarimeter. Polariscopic images are simulated from Mueller measurements of 19 other human subjects to test the robustness of this optimal solution.

Effects of typical liquid-crystal retarder errors on optimized Stokes polarimeters

Liquid crystal variable retarders (LCVRs) are often used in Stokes polarimeters as they allow the measurement of different polarization components by applying an electric field that manipulates the induced retardance. However, the optical retardance introduced by these devices is in general not homogenous across the aperture. Another problem with this type of devices is that the fast-axis orientation is not homogenous, and it changes with the applied voltage. For the optimization of polarimeters, in terms of the noise amplification from the intensity measurements to the polarimetric data, the condition number (CN) is often used, but the effects of LCVR spatial variations are not considered. This paper analyzes the impact of errors in LCVRs in a set of optimized Stokes polarimeters simulated by adding errors in the induced retardance and fast-axis orientation. Then, the CN is calculated to observe the effect of these errors on the optimization. We show how errors in the LCVRs lead to different impacts in the polarimetric measurements for different optimized polarimeters, depending on their experimental parameters. Furthermore, we present the propagation error theory to choose the best experimental parameters to reduce the nonideal effects in optimized polarimeters.

Robust weighted principal components analysis demodulation algorithm for phase-shifting interferometry

We present an asynchronous phase-shifting demodulation approach based on the principal component analysis demodulation method that is robust to typical problems as turbulence, vibrations, and temporal instabilities of the optical setup. The method brings together a two-step and a phase-shifting asynchronous demodulation method to share their benefits while reducing their intrinsic limitations. Thus, the proposed approach is based on a two-fold process. First, the modulating phase is estimated from a two-step demodulation approach. Second, this information is used to compute weights to each phase-shifted pattern of the interferogram sequence, which are used in a novel weighted principal component demodulation approach. The proposed technique has been tested with simulated and real interferograms affected by turbulence and vibrations providing very satisfactory results in challenging cases.

Characterization of retardance spatial variations over the aperture of liquid-crystal variable retarders

We present a comparison of two experimental methods to measure retardance as a function of applied voltage and as a function of position over the aperture of liquid-crystal variable retarders. These measurements are required for many applications, particularly in polarimetry. One method involves the scan of an unexpanded laser beam over the aperture, and the other uses an expanded beam from a LED and a CCD camera to measure the full aperture with a single measurement. The first method is time consuming, is limited in the measured spatial resolution, and requires more expensive equipment to perform the scan, whereas the second method is low cost, with the spatial resolution of the CCD, and fast, but in principle has variations of the incident beam over the aperture that affect the measured retardance values. The results obtained show good agreement for the average values of retardance for the two methods, but the expanded-beam method shows more noise, particularly close to the voltage values at which the variable-retarder retardance versus voltage curves are unwrapped. These retardance variations can be reduced by smoothing the retardance image, which makes the expanded-beam method an attractive method for polarimetry applications since it gives the complete information in the full aperture of the device with the additional advantages of low cost, simplicity, and being less time consuming.

Fast Method for Liquid Crystal Cell Spatial Variations Estimation Based on Modeling the Spectral Transmission

Liquid crystal phase retarders are utilized by photonic devices and imaging systems for various applications, such as tunable filtering, light modulation, polarimetric imaging, remote sensing and quality inspection. Due to technical difficulties in the manufacturing process, these phase retarders may suffer from spatial non-uniformities, which degrade the performance of the systems. These non-uniformities can be characterized by measuring the spectral transmission at each voltage and each point on the liquid crystal cell, which is time consuming. In this work, we present a new fast and simple method for measuring and computationally estimating the spatial variations of a liquid crystal phase retarder with planar alignment. The method is based on measuring the spectral transmission of the phase retarder at several spatial locations and estimating it at others. The experimental results show that the method provides an accurate spatial description of the phase retarder and can be employed for calibrating relevant systems.

Optimization for liquid crystal variable retarder-based spectroscopic polarization measurements

We present an approach for improving liquid crystal variable retarder (LCVR)-based spectroscopic polarization measurements. As deduced mathematically, the transfer coefficients from the random intensity noise to the signal noise are functions of modulation parameters of the LCVR, i.e., modulation range (MR) and initial retardation. Simulations allow more details about the roles of two parameters. A broad MR reduces effectively the values of the coefficients and leads to a better signal quality. However, as the MR narrows, initial retardation begins to influence the signal quality. To obtain a high-quality spectrum, a recommended solution is to settle the MR more than π at each wavelength. This treatment has two advantages: non-sinusoidal modulation becomes possible and the modulations do not average to zero. Moreover, it weakens the interference of non-uniform intensity distribution in wavelengths of the signal spectrum. These conclusions are proven in experiments. Further, this approach is valid for other polarimeters and ellipsometers based on LCVRs.